Vermont phÅ“nix. [volume] (Brattleboro, Vt.) 1834-1955, 1887-07-15
The Teaching of Arithmetic.


mctic in the Schools. he took the ground
that the system Of arithmetical teaching
which has grown up in the last score of
years is "A false one in that it does not prop
erly train the children in the fundamental
processes Of arithmetic, while it draws ex-
travagantly on their resources Of time,
strength and nervous energy 1t is one Of
the gravest accusations, he said. brought
against our modern school methods that the
old-fashioned readiness and correctness in
'ciphering' have been largely sacrificed to
the numerous technical applications and
difficult logical puzzles that have been in
troduced into the study of arithmetic
Children leave school i'll prepared to foot up
columns of figures, though able to work out
useless puzzles and to perform all sorts of
mathematical gymnastics One-fifth of the
school time, and often more. is devoted to
the study of arithmetic, as the schools are
now managed, and the worst of it is that
after the children have been worried, nag
ged, fretted, discouraged and worn out by
being compelled to go through all sorts of
abstruse and useless processes their drill
has not been such that they can be relied
on to perform the simple operations in num-
bers with accuracy.
The main thing which the school teaching
of arithmetic should aim at is to secure ac-
curacy and a reasonable degree of facility
in plain, ordinary ciphering Who of us
President Walker asked. has not seen in the
hands Of children eleven, twelve and thir-
teen years of age, examples in compound
and complex fractions which were more
difficult than any operation which any bank
cashier in the city of Boston has occasion to
perform in the course of his business from
January to December The most Jagged
fractions, such a. would hardly ever be
found in actual business operations-for ex-
ample, 1929 or 13-27-are piled one on top
OF another to produce an unreal and impos-
sihle difficulty; and the child, having been
furnished with such an arithmetical mon
strosity, is set to multiplying or dividing it
by another compound and complex frac-
ton as unreal and ridiculous as itself. All
this sort of thing in the teaching of young
children is useless and mschiovous. 1t is
bad psychology, bad physiology and bad
pedagogics. Every pupil, by the time he
leaves the grammar school, should he taught
to use small sums mfallibly, in multiplied
ton and division, and to add columns of
figures as long as an ordinary housekeepers
book or bank deposit book, almost beyond
the possibility of ever committing an error.
This nearly every child of ordinary bright
ness can be brought to do, and that in a
small part of the time now devoted to the
50 called study of arithmetic 1t is not nee
essary that the pupil should be brought to
do this thing with rapidity; only reason
able facility should be aimed at. If boy
is tn 90 into some line of work where fig
ures are used only incidentally and occa-
,ionally, he will have facility enough for the
purpose if, on the other hand, boy is to
20 into a position where his nam work i,
to he concerned with figures, he will readily
enough acquire the necessary facility, if
only accuracy has been secured during the
years Of especial mental growth and train
ing.
The master Of one Of our high schools
told me recently that he was informed by
the president of Boston bank that, at an
examination held during the year with ref
erence TO an appointment in his institution
out of several graduates of various high
schools of this vicinity, not one was found
able to add the columns Of figures given him
without errors, 1t is little wonder that thi.
should be the result, when, of the necessa.
t.ilx -, Il 4
| four-iifths or nine-tenths are occupied by
technical applications of numerical princi
| pies, or are worse than wasted by logical
| puzzles unsuited to the child's age and men.
tai strength. And this last remark bring,
me to the hardest accusation which is to be
brought against the current teaching OF
arithmetic Well aware that at this point
we have TO encounter an inveterate super.
| stitlon of the New England mind, ! have
| armed myself as much as possible with au
| thorltY derived from men of the ripest wis
| dom and the largest learning in mental sci
| ence. The charge | make against the ex
listing course Of study is that it is largely
made up of exercises which are not exer.
cises in arithmetic at all, or principally. but
are exercises in logic; and secondly. that a.
exercises in logic these are either useless OF
mischievous"
All this and much more of the same sort
Gen. Walker said, and his conclusions il
the final summing up were that all practica
and illustrative problems should be of ma
| ture TO interest and to aid the pupils il
their strictly arithmetical work, not t,
throw obstacles in their way or to increas,
the difficulty Of that work, it being express
ly provided that all problems where an at
tentive and diligent pupil of ordinary ca
pacity would find any considerable degre,
| of difficulty in making the statement" pre-
liminary TO the performance of the numeri
cal operations required, shall be deemed OBJ
iectionable
The result of the agitation of this subject
in the Boston school board has been deci
siye vote 10 reduce the time devoted t,
arithmetic in the public schools of the city
and to simplify the processes of instruction
Every person of mature years remember,
how in his childhood and youth he used t.
he tortured, or torture himself with pro
cesses in numbers, the operations in which
can only he lkened in their seeming 10 tn,
young mind TO a sort of benumbed CROPPING
in the dark and every such person ais,
remembers how, as his maturer years came
a new light broke in, sometimes suddenly
and what had been before only half com
| pretended now became as clear as MONDAY
There is food for thought for other school,
than those Of Boston in what Gen. Walker
says and in the action which the Boston
school board has taken under his lead